Elastoplastic nonlinear behavior of planar steel gabled frame

  • Moghaddam, Sina Heyrani (Department of Civil Engineering, Ferdowsi University of Mashhad) ;
  • Masoodi, Amir R. (Department of Civil Engineering, Ferdowsi University of Mashhad)
  • Received : 2019.03.08
  • Accepted : 2019.07.02
  • Published : 2019.10.25


In this paper, static nonlinear analysis of gable frame is performed using OpenSees software. Both geometric and material nonlinearities are considered in analyses. To consider large displacements, co-rotational coordinate transformation is used in software. The effects of symmetric and asymmetric support conditions including clamped and simple supports are studied. On the other hand, the material nonlinearity is reflected on analyses using Giuffre-Menegotto-Pinto steel material. Note that strain hardening characteristics are also considered in this model. Moreover, I-shaped cross-section is assumed for all members. The results are provided for different geometry properties of gable frame including shallow and deep inclined roof. It should be added that buckling and post-buckling behaviors of gable frame are investigated using related equilibrium paths. A comparison study is also implemented on the responses of buckling loads obtained for different support and geometry conditions. To trace snap-through paths completely, a displacement control method entitled arc-length is utilized. Findings show the capability of proposed model in nonlinear analysis of gable frames.


  1. Abbasnia, R. and A. Kassimali (1995), "Large deformation elastic-plastic analysis of space frames", J. Construct. Steel Res., 35(3), 275-290.
  2. Atlayan, O. and F. A. Charney (2014), "Hybrid buckling-restrained braced frames", J. Construct. Steel Res., 96, 95-105.
  3. Batoz, J.L. and G. Dhatt (1979), "Incremental displacement algorithms for nonlinear problems", J. Numeric. Method. Eng., 14(8), 1262-1267.
  4. Care, R. F., R. E. Lawther and A. P. Kabaila (1977), "Finite element post-buckling analysis for frames", J. Numeric. Method. Eng., 11(5), 833-849.
  5. Chan, S. L. and G. W. M. Ho (1994), "Nonlinear Vibration Analysis of Steel Frames with Semirigid Connections", J. Struct. Eng., 120(4), 1075-1087.
  6. Chen, H. H., W. Y. Lin and K. M. Hsiao (2006), "Co-rotational finite element formulation for thin-walled beams with generic open section", Comput. Methods Appl. Mech. Eng., 195(19), 2334-2370.
  7. Clarke, M. J. and G. J. Hancock (1990), "A study of incremental-iterative strategies for non-linear analyses", J. Numeric. Method. Eng., 29(7), 1365-1391.
  8. Crisfield, M. A. (1983), "An arc-length method including line searches and accelerations", J. Numeric. Method. Eng., 19(9), 1269-1289.
  9. Dere, Y. and F. Dede (2011), "Nonlinear finite element analysis of an R/C frame under lateral loading", Math. Comput. Appl., 16(4), 947.
  10. El-Zanaty, M. H. and D. W. Murray (1983), "Nonlinear finite element analysis of steel frames", J. Struct. Eng., 109(2), 353-368.
  11. Fafard, M. and B. Massicotte (1993), "Geometrical interpretation of the arc-length method", Comput. Struct., 46(4), 603-615.
  12. Filippou, F. C., V. V. Bertero and E. P. Popov (1983), "Effects of bond deterioration on hysteretic behavior of reinforced concrete joints", NSF/CEE-83032, Earthquake Engineering Research Center, University of California, Richmond, CA, USA.
  13. Fu, Z., K. Ohi, K. Takanashi and X. Lin (1998), "Seismic Behavior of Steel Frames with Semi-Rigid Connections and Braces", J. Construct. Steel Res., 46(1-3), 440-441.
  14. Giuffre, A. (1970), "Il comportamento del cemento armato per sollecitazioni cicliche di forte intensita", Giornale del Genio Civile, Istituto di Tecnica Delle Costruzioni, Facolta Di Architettura, Universita Degli Studi di Roma, Italy.
  15. Goldberg, J. E. and R. M. Richard (1963), "Analysis of non linear structures", J. Struct. Divison, 89(4), 333-351.
  16. Haisler, W. E., J. A. Stricklin and J. E. Key (1977), "Displacement incrementation in non-linear structural nalysis by the self-correcting method", J. Numeric. Method. Eng., 11(1), 3-10.
  17. Hsiao, K. M., J. Y. Lin and W. Y. Lin (1999), "A consistent co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams", Comput. Methods Appl. Mech. Eng., 169(1), 1-18.
  18. Jeon, H.M., Y. Lee, P.S. Lee and K.J. Bathe (2015), "The MITC3+ shell element in geometric nonlinear analysis", Comput. Struct., 146, 91-104.
  19. Kassimali, A. and J. J. Garcilazo (2010), "Geometrically nonlinear analysis of plane frames subjected to temperature changes", J. Struct. Eng., 136(11), 1342-1349.
  20. Liang, K., M. Ruess and M. Abdalla (2016), "Co-rotational finite element formulation used in the Koiter-Newton method for nonlinear buckling analyses", Finite Element Anal. Design 116, 38-54.
  21. Masoodi, A. R. (2018), "Analytical solution for optimum location of belt truss in outrigger system based on stability analysis", Proceedings of the Institution of Civil Engineers-Structures and Buildings, 172(5), 382-388.
  22. Masoodi, A. R. and S. Heyrani-Moghaddam (2015), "Nonlinear dynamic analysis and natural frequencies of gabled frame having flexible restraints and connections", KSCE J. Civil Eng., 19(6), 1819-1824.
  23. McKenna, F., G. Fenves and M. Scott (2006), "OpenSees: Open system for earthquake engineering simulation", Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA.,
  24. Memon, B.-A. (2004), "Arc-length technique for nonlinear finite element analysis", J. Zhejiang U Sci., 5(5), 618-628.
  25. Menegotto, M. and P. Pinto (1973), "Method of analysis for cyclically loaded reinforced concrete plane frames including changes in geometryand non-elastic behavior of elements under combined normal force and bending", Proceedings of IABSE Symposium on Resistance and Ultimate Deformability of Structures Acted on by Well-Defined Repeated Loads, Lisboa, Portugal.
  26. OpenSees (2006), University of California, Berkeley, USA.
  27. Oran, C. and A. Kassimali (1976), "Large deformations of framed structures under static and dynamic loads", Comput. Struct., 6(6), 539-547.
  28. Ottaviani, M. (1975), "Three-dimensional finite element analysis of vertically loaded pile groups", Geotechnique, 25(2), 159-174.
  29. Paullo Muoz, L. F., P. B. Gonalves, R. A. M. Silveira and A. Silva (2017), "Nonlinear resonance analysis of slender portal frames under base excitation", Shock Vib., 2017, 21.
  30. Powell, G. and J. Simons (1981), "Improved iteration strategy for nonlinear structures", J. Numeric. Method. Eng., 17(10), 1455-1467.
  31. Rezaiee-Pajand, M., E. Arabi and A. R. Masoodi (2018), "A triangular shell element for geometrically nonlinear analysis", Acta Mechanica, 229(1), 323-342.
  32. Rezaiee-Pajand, M. and A. R. Masoodi (2018), "Exact natural frequencies and buckling load of functionally graded material tapered beam-columns considering semi-rigid connections", J. Vib. Control., 24(9), 1787-1808.
  33. Rezaiee-Pajand, M. and A. R. Masoodi (2019), "Stability analysis of frame having FG tapered beam-column", J. Steel Struct., 19(2), 446-468.
  34. Rezaiee-Pajand, M., A. R. Masoodi and M. Bambaeechee (2018), "Tapered beam-column analysis by analytical solution", Proceedings of the Institution of Civil Engineers-Structures and Buildings, 1-16.
  35. Rezaiee-Pajand, M., A. R. Masoodi and M. Mokhtari (2018), "Static analysis of functionally graded nonprismatic sandwich beams", Adv. Comput. Design., 3(2), 165-190.
  36. Rezaiee-Pajand, M., M. Mokhtari and A. R. Masoodi (2018), "Stability and free vibration analysis of tapered sandwich columns with functionally graded core and flexible connections", CEAS Aeronautical J., 9(4), 629-648.
  37. Rezaiee-Pajand, M., N. Rajabzadeh-Safaei and A. R. Masoodi (2019), "An efficient mixed interpolated curved element for geometrically nonlinear analysis", Appl. Math. Modell., 76, 252-273.
  38. Rezaiee-Pajand, M., N. Rajabzadeh-Safaei and A. R. Masoodi (2019), "Linear and geometrically nonlinear analysis of plane structures by using a new locking free triangular element", Eng. Struct., 196, 1-19.
  39. Rezaiee Pajand, M., A. Masoodi and A. Alepeighambar Moghadam (2018), "Lateral-torsional buckling of functionally graded tapered I-beams considering lateral bracing", Steel Compos. Struct., 28(4), 403-414.
  40. Rodrigues, F. C., A. C. Saldanha and M. S. Pfei (1998), "Non-linear Analysis of Steel Plane Frames with Semirigid Connections", J. Construct. Steel Res., 46, 94-97.
  41. Rose, G., D. Nguyen and B. Newman (2016), "Implementing an arc-length method for a robust approach in solving systems of nonlinear equations", IEEE South East Conference, Norfolk, VA, USA. July.
  42. Salawdeh, S. and J. Goggins (2013), "Numerical simulation for steel brace members incorporating a fatigue model", Eng. Struct., 46, 332-349.
  43. Shi, G. and S. N. Atluri (1989), "Static and Dynamic Analysis of Space Frames with Nonlinear Flexible Connections", J. Numeric. Method. Eng., 28, 2635-2650.
  44. Shooshtari, A., S. Heyrani-Moghaddam and A. R. Masoodi (2015), "Pushover analysis of gabled frames with semi-rigid connections", Steel Compos. Struct., 18(6), 1557-1568.
  45. Shooshtari, A., A. Masoodi and S. H. Moghaddam (2014), "Free vibration analysis of gabled frame considering elastic supports and semi-rigid connections", J. Civil, Environ. Struct. Construct. Architect. Eng., 8(6), 701-705.
  46. Taeprasartsit, S. (2013), "Nonlinear free vibration of thin functionally graded beams using the finite element method", J. Vib. Control., 21(1), 29-46.
  47. Thombare, C. N., K. K. Sangle and V. M. Mohitkar (2016), "Nonlinear buckling analysis of 2-D coldformed steel simple cross-aisle storage rack frames", J. Build. Eng., 7, 12-22.
  48. Urthaler, Y. and J. N. Reddy (2005), "A corotational finite element formulation for the analysis of planar beams", Communications Numeric. Methods Eng., 21(10), 553-570.
  49. Wood, R. D. and O. C. Zienkiewicz (1977), "Geometrically nonlinear finite element analysis of beams, frames, arches and axisymmetric shells", Comput. Struct., 7(6), 725-735.